The class of Dirichlet random vectors is central in numerous probabilistic and statistical applications. The main result of this paper derives the exact tail asymptotics of the aggregated risk of powers of Dirichlet random vectors when the radial component has df in the Gumbel or the Weibull...

Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and statistical inference. In this paper we consider in the high-dimensional setting optimal estimation of the...

For nonbinary response variable depending on a finite collection of factors with values in a finite subset of R the problem of the optimal forecast is considered. The quality of prediction is described by the error function involving a penalty function. The criterion of almost sure convergence...

This paper presents a Hayashi–Yoshida-type estimator for the covariation matrix of continuous Itô semimartingales observed with noise. The coordinates of the multivariate process are assumed to be observed at highly frequent non-synchronous points. The estimator of the covariation matrix is...

We establish sufficient conditions for the asymptotic normality of kernel density estimators applied to causal linear random fields, by m-dependent approximation. Our conditions on the coefficients of linear random fields are weaker than the known results, although our assumption on the...

If covariates are measured with errors, failure to account for that errors may result in a biased estimator of the parameters and consequently the test based on the corresponding estimator may turn out to be biased under the non-zero null hypothesis. In this paper we derive score tests for...